Questions tagged [options]
A contract that gives the owner the right, but not the obligation, to buy or sell a security at a fixed price in the future.
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Shape of FX Volatility Surface
I'm familiar with the volatility surface for equity options with the smile/skew dynamic and flattening with increased maturity, and the explanation/intuition behind its shape. However, today I came ...
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How to compute Vega in the Heston Model
I am computing European Option Sensitivity as: Delta, Vega and Gamma. I am using Heston Model to simulation spot and the variance.
While computing Delta and Gamma, I understand, we need to bump spot ...
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Iron Butterfly Relationship with Butterfly
I'm reading Natenburg's Options book, and I'm not understanding why "Buying a traditional butterfly is equivalent to selling an iron butterfly," because later in the text Natenburg says that ...
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Working with wide bid ask spreads in option pricing model
I'm trying to fit an Heston model to market data. But market is data has some terms (<3M) with quite wide bid-ask spreads (12%-25%). Should I just use mid volatility? Is there maybe a model to pre-...
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Volatility surface
When fitting/calibrating a option model like heston to option data, what are some useful data handling to do?
The basic thing is to remove all options with no trade/volume, but how many maturities ...
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How would I find correlation / association of different time series datapoints with a target variable?
the title is a bit confusing.
Functionally, I have a dataset of N stocks containing options information, short information, and earnings information for each of the N stocks.
For each unique stock in ...
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Delta Hedging using another correlated asset
My question is about the following (from Maxime de Bellefroid, Ch. 5 The Greeks):
From my understanding $\Delta_2$ is the sensitive of the option (on the first instrument with underlying $S_1$) with ...
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If you continuously delta hedge a long option position will you be flat at expiry regardless of realized vol? [closed]
Learning about gamma and am confused about practical gamma trading strategies and struggling to understand how they can be monetized. Is all gamma just about setting limit orders above and below and ...
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"Forward" attribute for an option
I am downloading implied volatilities for some options. I noticed, however, that I am also able to choose "Forward" as an attribute for the option. What is this? Is it an option written on a ...
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Bloomberg field name to get implied volatility of options
I am trying to get option data from bloomberg api. I got the all available options on a given underlying eg:"ASML NA" and Field "PX_LAST" gave the last traded price for each option....
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difference between strike notional and spot notional
Can someone please explain the difference between strike and spot notional? in the context of equity options trading?
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Butterfly price bound independent on underlying distribution
Assuming no fees and interest rate $r=0$%, what is the most you would be willing to pay for a \$103/\$106/\$108 European call fly, regardless of the underlying distribution? Buying the fly in this ...
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Option Prices And Calibrating The Heston Model Code Question
I'm trying to understand this Python code that uses Quantlib to calibrate the parameters of the Heston model. The data that is provided in the code is the spot price, the risk free interest rate, the ...
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Does Black-Scholes imply that the expected return for an asset is fixed as the volatility increases? [closed]
I'm new to this, and just trying to understand what options prices imply about asset growth. I'm looking at the following expression for the underlying asset price in the Black-Scholes model, in ...
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QuantLib including holiday in option price
I am trying to add a holiday to my calendar in QuantLib such that my option pricing model considers this in pricing where I would expect that the time to expiry should decrease with the inclusion of a ...
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Calculating the PnL of a delta-hedged option at a point in time
In a BS world (constant volatility, no transaction costs, continuous hedging) If I buy or sell an option and continuously delta-hedge, I know how to calculate the final expected PnL based on implied ...
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Time steps in CRR Binomial Option Pricing for American Options
how do you determine the time steps required as inputs to the Cox Rubinstein Binomial Option Pricing model when trying to determine the fair price of an American option? Most textbooks and literature ...
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Calculate Value at Risk for a futures contract or option position [closed]
How could we calculate VaR for a futures contract or a option position? I know that a VaR is calculated by the return multiply the investment amount, but how could we calculate the investment amount ...
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ESSVI calibration problem in translating parameter bounds
I am trying to implement the calibration algorithm presented in the "ESSVI Implied Volatility Surface" white paper from Factset by Akhundzadeh et al.
The eSSVI model includes 2 variables ...
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Pricing Option with Payoff of $S_T$ units of a European Digital Call [duplicate]
I am in a Black Scholes market with the usual riskless asset $B$ and risky asset $S$ with dynamics given by
\begin{align*}
dB_t &= rB_t dt, B_0 = 1, \\
dS_t &= rS_t dt + \sigma S_t dW_t^{\...
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What is the arbitrage opportunity and strategy here? [closed]
Suppose that the current stock price is $€100$, the exercise price is $€100$, the annually compounded interest rate is 5 percent, the stock pays a $€1$ dividend in the next instant, and the quoted ...
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What is the meaning of Domestic Exchange Rate here?
So I have the following formula for the Pricing of a Quanto Option (see image below).
While I understand this formula pretty well, I am not sure what is referred to as "domestic exchange rate&...
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Calculating PnL of Options strategies with Volatility Surface
New to Vol trading - wondering if there are any good references on calculating PnL from options strategies if I only have a volatility surface (delta or moneyness) and no individual options prices.
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Representing a continuous time hedge discretely
I recently came across an example (Section 5.2.9 here) which does a simple delta hedging experiment. Below are the details:
Market conditions
Interest rates are at a 2% level --> r = 0.02
The ...
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How can I derive the price of american options given the european options prices? [closed]
I have the european volatility surface of a given asset. What is the correct procedure to compute the price of the options with american exercise type?
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How do sell-side institutions manage interest rate derivatives books in practice?
I'm interested in real practices of hedging interest rate caps and floors. There are plenty of articles explaining pricing of interest rate derivatives, but not so many explaining hedging such ...
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How can I use SPX options volatility surface to derive SPY options prices? [duplicate]
I am trying to figure out what is the correct procedure one can use to derive the prices from SPY options given the prices of SPX options.
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Why does Natenberg say that when future options with future-type settlement are traded, no money changes hands?
I feel I am fundamentally misunderstanding something when it comes to options on futures. On the bottom of page 98 of 2nd edition Option volatility and Pricing by Natenberg he says:
"In the US, ...
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Call option on forward [closed]
What is the trade description behind a call option on a forward? How can it be described with words and not with mathematical formulas?
So what is the intuition behind the following payoff:
$$Payoff_{...
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No expected return in Black Scholes formula: But how about the gamma?
A lot has been written about the fact that the expected return of the underlying asset is not part of the Black Scholes formula. I understand the argument that the performance of the underlying asset ...
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Bond Option: Cash Price or Quoted Price as Underlying
John Hull mentioned in his book using Cash Price(Dirty Price) instead of Quoted Price(Clean Price) in pricing a bond option using Black-Scholes. It confuses me as it seems more natural to assume the ...
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Characteristic Function Kou (2002) Model
I'm looking for the correct characteristic function for the Kou (2002) jump diffusion model.
Can someone help me? Because if I try to look at it online everyone forgot $r$ and $S_0$.
This is what I ...
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Determining Stock Price Distribution [closed]
I am trying to derive a Stock Price Distribution for a particular time frame. Meaning thereby, let's say Market is about to close in 30 minutes and I want to calculate Stock Price Distribution for the ...
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Practical risk management on snowball autocallable portfolios
I am new to exotic options pricing and risk management. The scenario that I encounter is that the market maker sells snowball autocallable products(accumulated coupon) every trading day and has to ...
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Find strike of an option based on a delta without option price
I would like to use the Black Scholes model to get the strike based on delta, without having the option price.
So I read this: From Delta to moneyness or strike
Which show that we can get a strike ...
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$\mathbb{Q}$ measure and $\mathbb{P}$ measure, trading strategy
I just want to be sure if my thinking is correct and does not have any flaws.
Let's define stock as a process $S$ (see the picture below) with real-world measure $\mathbb{P}$, where $p=0.9$ and Bonds ...
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Book Recommendations on Options Derivatives [duplicate]
I want to learn about Options Derivatives and am looking for an introductory (as much as possible) book to start with. Any recommendations?
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University Problem about interpolation Implied volatility BS Model (volatility smile)
Good morning,
this is my first question on this forum, I'm writing from Milan (Italy) and I have a question about a University Problem.
The problem is about entering in a Long Range Forward (buy a ...
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How to find volatility of a 1 day option based on 2 day annualized volatility
first time -I'm curious as to how the following would work:
I have a 2 day(only includes full day of Thursday and Friday) swaption with a volatility of 100 bps.
We also know the weights we've assigned ...
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Do calls and puts have the same strikes? [closed]
This question may seem basic but it is not. It concerns about the details of the market structure. So please do not rush to close it. Consider the (liquid) options on a very liquid underlying, say the ...
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Does the CME Option on 1M SOFR keep trading in the compounding period
I am working with implied vol surfaces for money market options and trying to understand the dynamics of the CME's options on one-month SOFR futures. I want to establish whether trading ceases before ...
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How to fit KDE from existing probability density function values
I am working with options data, and I am using Breeden-Litzenberger formula to derive the risk-neutral terminal stock price PDF.
After applying the formula, here is a scatter plot of strike price vs ...
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Can the break-even of a straddle be lower than the implied move?
Let us consider a two day option:
1 day having a baseline vol of 16%
1 day having an event for which we want to find the implied move, higher than 16%
Is it possible that the price of the straddle ...
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Can european call option on stock have positive theta? (assume positive interest rate)
I believe the answer is no, as minimum value of call option is S - PV(K), which can never be below S-K.
The reason for the question is this paragraph in Natenberg, pg 109:
Is it ever possible for an ...
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How does a principal protected note pay the return on the market, on the whole principal? [closed]
A real life principal protected note pays exactly the index return with 50% participation and a max 3y return of 30%:
total_principle*(end_price/start_price-1)*50%
These are all of the features, ...
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Mean instantaneous drift from option prices
I'm going through the paper "Pricing European Options in Realistic Markets" by Schaden (2002) as its formulation for instantaneous mean drift seemed really interesting.
On page 14, the ...
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Does the risk neutral pdf that is derived using Litzenberger-Breeden Method correspond to gamma and it's integral correspond to delta?
I derived the pdf using the butterfly prices and the curve looks like gamma of an option at every strike. Is that the case or am I missing something to get the pricing of an option?
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How to price PIK (paid-in-kind) coupon bond with option by the borrower to pay cash?
I'm trying to price a PIK coupon with an Embedded Option by the borrower to pay in cash. Without the Embedded Option, it is simply a zero-coupon bond paying Principal*(1 + coupon rate)^n at the end.
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Move from risk-neutral probability to historical probability
I am working on a density forecasting project using options. Using the Breeden-Litzenberger formula it is possible to find the implied density at maturity under the risk neutral probability of an ...
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What is the minimum price of an option, given no information about Greeks? [closed]
I was asked this interview questions for an analyst level structuring role and it has been bothering me since I can't figure it out:
Assuming the price of an equity is 100, what is the minimum price ...
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